基于不相交码的严格几乎最优弹性函数构造OA

Boolean functions are served as crucial nonlinear components in stream cipher systems.To safeguard the entire system against various attacks,such as the best affine approximation attack,correlation attack,and algebraic attack,they need to meet several cryptographic criteria,including high nonlinearity,a certain order of resilience,and good algebraic properties.Nevertheless,there exists a trade-off between the resilience and nonlinearity of Boolean functions.Therefore,constructing resilient Boolean functions with high nonlinearity has always been a significant challenge in the field of cryptographic function design.This study draws inspiration from the traditional Maiorana-McFarland(M-M)class construction approach and utilizes a special class of disjoint code structures to construct a family of Boolean functions with alternating Walsh spectrum distributions.These functions are then cascaded,followed by necessary modifications,ultimately leading to a method for constructing resilient Boolean functions with high nonlinearity.This method can extend balanced functions of k variables(where k≥6)with strictly almost optimal nonlinearity to functions of 3k variables and provides a constructive approach to modifying them into resilient functions without impairing nonlinearity.